Many search engine services, such as Google and Overture, provide for searching for information that is accessible via the Internet. These search engine services allow users to search for display pages, such as web pages, that may be of interest to users. After a user submits a search request (i.e., a query) that includes search terms, the search engine service identifies web pages that may be related to those search terms. To quickly identify related web pages, the search engine services may maintain a mapping of keywords to web pages. This mapping may be generated by “crawling” the web (i.e., the World Wide Web) to identify the keywords of each web page. To crawl the web, a search engine service may use a list of root web pages to identify all web pages that are accessible through those root web pages. The keywords of any particular web page can be identified using various well-known information retrieval techniques, such as identifying the words of a headline, the words supplied in the metadata of the web page, the words that are highlighted, and so on. The search engine service identifies web pages that may be related to the search request based on how well the keywords of a web page match the words of the query. The search engine service then displays to the user links to the identified web pages in an order that is based on a ranking that may be determined by their relevance to the query, popularity, importance, and/or some other measure.
Three well-known techniques for page ranking are PageRank, HITS (“Hyperlinked-Induced Topic Search”), and DirectHIT. PageRank is based on the principle that web pages will have links to (i.e., “outgoing links”) important web pages. Thus, the importance of a web page is based on the number and importance of other web pages that link to that web page (i.e., “incoming links”). In a simple form, the links between web pages can be represented by adjacency matrix A, where Aij represents the number of outgoing links from web page i to web page j. The importance score wj for web page j can be represented by the following equation:
      w    j    =            ∑      i        ⁢                  A        ij            ⁢              w        i            
This equation can be solved by iterative calculations based on the following equation:ATw=wwhere w is the vector of importance scores for the web pages and is the principal eigenvector of AT.
The HITS technique is additionally based on the principle that a web page that has many links to other important web pages may itself be important. Thus, HITS divides “importance” of web pages into two related attributes: “hub” and “authority.” “Hub” is measured by the “authority” score of the web pages that a web page links to, and “authority” is measured by the “hub” score of the web pages that link to the web page. In contrast to PageRank, which calculates the importance of web pages independently from the query, HITS calculates importance based on the web pages of the result and web pages that are related to the web pages of the result by following incoming and outgoing links. HITS submits a query to a search engine service and uses the web pages of the result as the initial set of web pages. HITS adds to the set those web pages that are the destinations of incoming links and those web pages that are the sources of outgoing links of the web pages of the result. HITS then calculates the authority and hub score of each web page using an iterative algorithm. The authority and hub scores can be represented by the following equations:
      a    ⁡          (      p      )        =                    ∑                  q          →          p                    ⁢                        h          ⁡                      (            q            )                          ⁢                                  ⁢        and        ⁢                                  ⁢                  h          ⁡                      (            p            )                                =                  ∑                  p          →          q                    ⁢              a        ⁡                  (          q          )                    where a(p) represents the authority score for web page p and h(p) represents the hub score for web page p. HITS uses an adjacency matrix A to represent the links. The adjacency matrix is represented by the following equation:
      b    ij    =      {                                                    ⁢            1            ⁢                                                                                                  ⁢                                          if                ⁢                                                                  ⁢                page                ⁢                                                                  ⁢                i                ⁢                                                                  ⁢                has                ⁢                                                                  ⁢                a                ⁢                                                                  ⁢                link                ⁢                                                                  ⁢                to                ⁢                                                                  ⁢                page                ⁢                                                                  ⁢                j                            ,                                                                                    ⁢            0                                                            ⁢            otherwise                              
The vectors a and h correspond to the authority and hub scores, respectively, of all web pages in the set and can be represented by the following equations:a=ATh and h=AaThus, a and h are eigenvectors of matrices ATA and AAT. HITS may also be modified to factor in the popularity of a web page as measured by the number of visits. Based on an analysis of click-through data, bij of the adjacency matrix can be increased whenever a user travels from web page i to web page j.
Since web sites are a primary organizational structure of the web, many web applications attempt to rank web sites based on their importance. For example, a search engine service may factor in the rank of a web site into the ranking of web pages of that web site. In particular, a web page of a highly ranked web site should be ranked higher than a web page of a less highly ranked web site, assuming all other features of the web pages are equal. Web sites have been ranked using web page ranking techniques that are applied to web sites. Typically, the web sites are represented as a web graph with web sites represented as vertices of the graph and links between web pages of the web sites represented as edges between the vertices. A web graph can be represented as an adjacency matrix as described above and a web page ranking algorithm can be applied to the adjacency matrix to generate a ranking of the web sites. Unfortunately, such an approach to ranking web sites results in a ranking that many times does not reflect the relative importance of the web sites.